Infrared renormalons and $1/Q^2$ power corrections in deep-inelastic sum rules are studied. The renormalization of operators with power divergence are discussed. The higher-twist terms in the operator product expansion are shown to account for the residual
representing a link,starting at the discrete point n and ending at a neighbouring lattice point in the direction ?µ.P is the path-ordering operator.I de?ne an operator on lattice,O 4α(Λ2,n )=i Λ2
π2
µν sin k µπΛ k µk 4d 4k π2¯u γµγ5u.(25)
The calculation is done with Feynman rules in Euclidean space.From this we get the one-loop contribution to the coe?cient function,
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